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CSC 281Discrete Mathematics for Computer Science

Dr.Yuan Tianytian@ksu.edu.sa

Syllabus

Course Overview

• Course title: Discrete mathematics for Computer Science • Instructors:

– Dr. Yuan Tian (ytian@ksu.edu.sa) —Course Coordinator• Office Hour : Sun. Tue. Thu.(11:00-13:00), Mon.(9:00-

13:00)– Ms.Noura AlAngari (nmalangari@ksu.edu.sa)• Office Hour : Sun. Tue. Thu. (9:00 – 12:00)

• Credit hours: 3 Hours Lecture/week 1 Hour Tutorial/week• Prerequisite

– Engineering Probability & Statistics – Data structure

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Textbook

Discrete Mathematics and Its Applications by Kenneth H. Rosen

Use lecture notes as study guide.

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Acknowledgement

• Most of these slides are adapted from ones created by Professor Bart Selman at Cornell University.

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Course Themes, Goals, and Course Outline

Goals of CSC 281Introduce students to a range of mathematical tools from discrete

mathematics that are key in computer science

Mathematical SophisticationHow to write statements rigorouslyHow to read and write theorems, lemmas, etc.

How to write rigorous proofs

Areas we will cover:Logic and proofsSet TheoryInduction and RecursionCounting and combinatoricsProbability theory

Number Theory Trees and Graphs Discrete Probability

Aside: We’re not after the shortest or most elegant proofs;verbose but rigorous is just fine!

Practice works!

Actually, only practice works!Note: Learning to do proofs fromwatching the slides is like trying tolearn to play tennis from watchingit on TV! So, do the exercises!

Topics of CSC 281Logic and Methods of Proof

Propositional Logic --- SAT as an encoding language!Predicates and QuantifiersMethods of Proofs

SetsSets and Set operationsFunctions

CountingBasics of countingPigeonhole principlePermutations and Combinations

Number Theory Modular arithmeticRSA cryptosystems

Topics of CSC 281

ProbabilityProbability Axioms, events, random variableIndependence, expectation, example distributionsBirthday paradox Monte Carlo method

Graphs and TreesGraph terminologyExample of graph problems and algorithms:

graph coloringTSPshortest path

Grading• Quizzes: 10 points • Tutorial: 10 points • Project(Presentation+report): 10 points • Midterm 1: 15 points • Midterm 2: 15 points • Final Exam: 40 points

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About Project…

• Content Use the methods you lean from CSC281 to solve a new problem (not

discussed in the slide)

• Requirements: 2 (or 1) students/group Final Report (Problem statement, Mathematical modelling, Complete

solution, Program(bonus) ) A detailed written report of the project should be submitted in the

first week after finishing all lectures.

Exam Dates• Quiz1: Oct.4 (Sunday) 13:00-14:00• Mid1: Oct. 20 (Tuesday )• Quiz2: Nov.15(Sunday) 13:00-14:00• Mid2:Dec . 8 (Tuesday)

Notes for Email Communication

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• Your email header must start with [section no.-CSC281]• Send your email to ytian@ksu.edu.sa /

nmalangari@ksu.edu.sa email address. • Please write your name and your ID at the end of the

email